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Traveling Wave Solutions for Complex Space-Time Fractional Kundu-Eckhaus Equation

Author

Listed:
  • Mohammed Alabedalhadi

    (Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan)

  • Mohammed Shqair

    (College of Science, Zarqa University, Zarqa 132222, Jordan)

  • Shrideh Al-Omari

    (Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Ajloun 26816, Jordan)

  • Mohammed Al-Smadi

    (Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan
    Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 20550, United Arab Emirates
    College of Commerce and Business, Lusail University, Doha 122104, Qatar)

Abstract

In this work, the class of nonlinear complex fractional Kundu-Eckhaus equation is presented with a novel truncated M-fractional derivative. This model is significant and notable in quantum mechanics with good-natured physical characteristics. The motivation for this paper is to construct new solitary and kink wave solutions for the governing equation using the ansatz method. A complex-fractional transformation is applied to convert the fractional Kundu-Eckhaus equation into an ordinary differential equations system. The equilibria of the corresponding dynamical system will be presented to show the existence of traveling wave solutions for the governing model. A novel kink and solitary wave solutions of the governing model are realized by means of the proposed method. In order to gain insight into the underlying dynamics of the obtained solutions, some graphical representations are drawn. For more illustration, several numerical applications are given and analyzed graphically to demonstrate the ability and reliability of the method in dealing with various fractional engineering and physical problems.

Suggested Citation

  • Mohammed Alabedalhadi & Mohammed Shqair & Shrideh Al-Omari & Mohammed Al-Smadi, 2023. "Traveling Wave Solutions for Complex Space-Time Fractional Kundu-Eckhaus Equation," Mathematics, MDPI, vol. 11(2), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:404-:d:1033785
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    References listed on IDEAS

    as
    1. Al-Smadi, Mohammed & Arqub, Omar Abu, 2019. "Computational algorithm for solving fredholm time-fractional partial integrodifferential equations of dirichlet functions type with error estimates," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 280-294.
    2. J. F. Gómez-Aguilar & Dumitru Baleanu, 2017. "Schrödinger equation involving fractional operators with non-singular kernel," Journal of Electromagnetic Waves and Applications, Taylor & Francis Journals, vol. 31(7), pages 752-761, May.
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    Cited by:

    1. Anwar Aldhafeeri & Muneerah Al Nuwairan, 2023. "Bifurcation of Some Novel Wave Solutions for Modified Nonlinear Schrödinger Equation with Time M-Fractional Derivative," Mathematics, MDPI, vol. 11(5), pages 1-14, March.

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